A precise characterization of optical components generally occurs via interferometric measurements. It is show in this paper that Fourier based deflectometry method can be used for very sensitive and precise wavefront reconstruction. The wavefront is expressed from the raw measurements of the wavefront derivatives as a Zernike polynomial expansion. The form of the polynomials permits absolute instrumental error characterization by repeated measurement of the element under test oriented at several azimuthal angles. It is shown in this paper that nanometric precision of Zernike based reconstructions can be performed and that the air turbulences are the experimental limiting factor to the instrumental precision.